8.3 problem Problem 3

Internal problem ID [2256]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number: Problem 3.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-y-10 \cos \relax (x ) {\mathrm e}^{2 x}=0} \end {gather*}

Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-y(x)=10*exp(2*x)*cos(x),y(x), singsol=all)
 

\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+c_{1} {\mathrm e}^{x}+{\mathrm e}^{2 x} \left (2 \sin \relax (x )+\cos \relax (x )\right ) \]

Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 33

DSolve[y''[x]-y[x]==10*Exp[2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^x+c_2 e^{-x}+e^{2 x} (2 \sin (x)+\cos (x)) \\ \end{align*}